Learning objectives
- Recognise, explain, and apply “μέτρηση γωνίας”.
- Recognise, explain, and apply “άξονας συμμετρίας”.
- Recognise, explain, and apply “μετασχηματισμοί”.
Greek Primary Grade 4 / Mathematics / Γεωμετρία
Γωνίες και συμμετρία: structured theory, worked examples, answered practice, and a mastery checklist for Greek Primary Grade 4.
Unit
The essential chapter ideas in a clear sequence before practice.
Mark every given on the diagram and state the target clearly. Start from a relationship that connects exactly those quantities.
Mathematics
Start with theory and core examples, then move to worked exercises and short test-style practice.
The structure follows the official textbook layout and is used to organise study.
The areas that usually create mistakes or need extra revision.
Every geometric step needs a property, theorem, or definition. A result without justification is not a complete proof.
Length, area, volume, and angle use different units. Round only at the end and keep sufficient intermediate precision.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Draw and label every given before choosing a property or formula. Finish with estimation, an inverse operation, or substitution as a check.
Mathematics
Follow the method step by step and check why every step is valid.
A rectangle is 12 cm long and 3 cm wide. Find its perimeter and, where covered, its area.
Perimeter 30 cm, area 36 cm².
Explain “μέτρηση γωνίας” in your own words and use a picture, objects, a table, or a simple measurement to support it.
A complete explanation connects the correct idea, a clear representation, and a sensible check.
Γωνίες και συμμετρία
Eight graded tasks from core fluency to exam-style application. Work independently before opening a hint or answer.
Calculate 9 + 3 and show two representations connected with “μέτρηση γωνίας”.
Use a number line, place value, or objects.
9 + 3 = 12. Valid representations include number-line jumps and grouped objects.
5 equal groups contain 5 objects each. Find the total and write an addition and multiplication statement.
Add 5 a total of 5 times.
5 + 5 + 5 + 5 + 5 = 5 · 5 = 25.
Continue 8, 10, 12, ... for three more terms and explain the rule.
Check how much each term increases.
14, 16, 18; +2.
A rectangle has sides 4 cm and 4 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 4 + 4 + 4 + 4 = 16 cm.
Out of 42 objects, 7 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
7/42 = 1/6.
The measurements are 3, 3, 3, and 3. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 3, least 3, range 0.
Anna has 30 cards, gives away 6, then shares the rest into 4 equal groups. How many are in each group?
Subtract first, then divide.
30 - 6 = 24; (24) : 4 = 6.
A learner says 9 + 2 = 12. Find the error, correct it, and check the correction.
Check with a number line or inverse subtraction.
9 + 2 = 11; 11 - 2 = 9.
Γωνίες και συμμετρία
Six distinct assignments from core fluency to challenge, each with an estimated time, hint, and answer guide.
Homework 1: Calculate 5 + 4 and show two representations connected with “μέτρηση γωνίας”.
Use a number line, place value, or objects.
5 + 4 = 9. Valid representations include number-line jumps and grouped objects.
Homework 2: 6 equal groups contain 8 objects each. Find the total and write an addition and multiplication statement.
Add 8 a total of 6 times.
8 + 8 + 8 + 8 + 8 + 8 = 6 · 8 = 48.
Homework 3: Continue 4, 7, 10, ... for three more terms and explain the rule.
Check how much each term increases.
13, 16, 19; +3.
Homework 4: A rectangle has sides 7 cm and 5 cm. Find its perimeter and explain why four sides are counted.
Opposite sides are equal.
Perimeter = 7 + 5 + 7 + 5 = 24 cm.
Homework 5: Out of 6 objects, 3 are shaded. What fraction is shaded and how does it simplify?
Put shaded objects over the total.
3/6 = 1/2.
Homework 6: The measurements are 6, 4, 6, and 4. Find the greatest, least, and range.
Range = greatest value minus least value.
Greatest 6, least 4, range 2.
35 minutes / 30 marks
A timed, full-mark self-assessment with model-answer guidance.
Start the timer when ready, work without notes, show every step, and open model answers only after finishing.
1. Calculate 3 + 4 and show two representations connected with “μέτρηση γωνίας”.
2 marks3 + 4 = 7. Valid representations include number-line jumps and grouped objects.
2. 6 equal groups contain 6 objects each. Find the total and write an addition and multiplication statement.
3 marks6 + 6 + 6 + 6 + 6 + 6 = 6 · 6 = 36.
3. Continue 9, 12, 15, ... for three more terms and explain the rule.
3 marks18, 21, 24; +3.
4. A rectangle has sides 5 cm and 5 cm. Find its perimeter and explain why four sides are counted.
4 marksPerimeter = 5 + 5 + 5 + 5 = 20 cm.
5. Out of 16 objects, 8 are shaded. What fraction is shaded and how does it simplify?
4 marks8/16 = 1/2.
6. The measurements are 4, 4, 4, and 4. Find the greatest, least, and range.
4 marksGreatest 4, least 4, range 0.
7. Anna has 42 cards, gives away 7, then shares the rest into 5 equal groups. How many are in each group?
5 marks42 - 7 = 35; (35) : 5 = 7.
8. A learner says 3 + 3 = 7. Find the error, correct it, and check the correction.
5 marks3 + 3 = 6; 6 - 3 = 3.
Unit
Curriculum reference sources. Always confirm the teaching sequence with the school and tutor.
Where to start: textbook, daily material, PDFs, videos, and worked examples.
Targeted practice before full tests so coverage is clear.
How to measure progress in this chapter and when it enters a cumulative mock.
What to do after finishing the chapter and how it connects to the next unit.
Note: for the official examinable syllabus of each school year, always confirm with the school, tutor, and current Ministry/IEP announcements.